How to make an object appear/visible along a path
To keep it simple, you might consider just using the native properties of Blender curves.

Note that in this example, the path-curve is not cyclic. It's made by converting a mesh ( a circle, scaled in Edit Mode in Y ) with one of its vertices V ripped, then converted to a curve with two ends at the same place.


A curve can have a renderable bevel profile .. either its own, (a circle with variable resolution) or another curve you assign for the purpose, which will be swept along its local Z.
The profile can be tapered along its length, using another curve
The start and end points of the bevel along the curve can be set, and animated. So the curve can be made to 'grow' along its length.
The taper can be mapped either to the entire curve, or just the part which is beveled.




The illustration shows a curve, its taper, and its profile.

Your hexagon can be given a Follow Path constraint along the main curve, with its 'Offset' animated in sync with the curve's Bevel End setting.



..or maybe with the taper mapped to the beveled section: